Solution (source code)

= Solution

For a lossless single interface at <normal incidence>, $R=1-T=0.04$ and the <Fresnel equations> give $R=[(n-1)/(n+1)]^2$, taking air's <refractive index> as one. Selecting the <glass> branch $n>1$ gives
$$
\boxed{n=\frac{1+\sqrt R}{1-\sqrt R}=1.50}.
$$
The reciprocal root $2/3$ is the mathematical lower-index branch, not ordinary <glass>.